Although not restricted thereto, the invention has utility in the control of aircraft in flight and particularly the control of aircraft in altitude variation. An altitude signal may, for example, change 40 millivolts per minute for a 400 foot per minute change in altitude. Assuming an aircraft can fly to 40,000 feet, then the total change of voltage with altitude will be 4 volts. To emphasize the problem of control of an aircraft having a 40,000 foot altitude limitation, the 40 millivolts per minute is equal to 0.00067 volts per second. It is recognized that this is an extremely small change for a 1 second time interval considering the change in altitude that an aircraft can achieve in a 1 second interval. This same problem of a very small incremental change for a unit of time is also present in other control situations where the controlled variable has the potential of changing over an extremely wide range.
Early attempts to deal with this problem utilized a simple rate network connected to the output of an amplifier. This circuit generates a rate signal at the output of the amplifier that varies with changes of an input signal. Considering the example given above where the input voltage changes 4 millivolts per minute or 0.00067 volts per second, and that a reasonable output would be 1 volt for a 0.00067 volt per second input, then the time constant required by the rate network would be equal to approximately 1500 seconds. A capacitor required to produce such a time constant in a rate network is impractical, but more importantly the time required for the rate circuit to initially stabilize would be several times the 1500 second time constant and could reasonably be 4500 seconds. That is, it would take 4500 seconds for the rate network circuit to achieve some semblance of stability for an initial input signal which, and particularly in aircraft control, is an unacceptable stabalizing time interval. Note that the component that has to initially stabilize when the circuit is first turned on is the voltage across the capacitor C in the expression: EQU Vout=(RC)(.DELTA.Vin/SEC)
In addition to a long initial stabilization time, a rate network operating as discussed above would require resistor components that are very unstable with temperature and further are costly. Also, for the rate network to be accurate, the leakage current of the capacitor element must be very low which again is an expensive item considering the size of the capacitor required. Thus, heretofore to provide an acceptable signal that changes over a wide dynamic range, a circuit with a long time constant was required having a capacitor with very low leakage characteristics. The rate network approach to expanding a signal that varies over a wide dynamic range has thus proven impractical.
With reference particularly to aircraft control, the rate network solution to the expansion of an input signal proved unacceptable considering that aircraft often fly through turbulent air conditions where an input signal relating to altitude may take on the characteristics of a step input. A step input change to a rate network with a long time constant would mean the aircraft could not be controlled until the circuit re-stabilized after saturating. In a rate network system in an aircraft air data application, normal system noise and turbulance could keep the rate network almost constantly in a state of non-linear, saturated operation, or recovery from a non-linear state. This would effectively make the resulting output signals useless.